Examples

Properties

Proposition

A geometric morphismf:ℱ→ℰf:\mathcal{F}\to\mathcal{E} is open iff the canonical map λ:Ωℰ→f*(Ωℱ)\lambda:\Omega_\mathcal{E}\to f_\ast(\Omega_\mathcal{F}) of poset objects in ℰ\mathcal{E} has an internal left adjoint μ:f*(Ωℱ)→Ωℰ\mu :f_\ast(\Omega_\mathcal{F})\to\Omega_\mathcal{E}.